A353563 -id:A353563 - cp's OEIS frontend

A353564 Product_{d|n, dA276086(phi(d)), where A276086 is primorial base exp-function, and phi is Euler totient function.

1, 2, 2, 4, 2, 12, 2, 12, 6, 36, 2, 108, 2, 20, 54, 108, 2, 180, 2, 972, 30, 180, 2, 8748, 18, 100, 30, 300, 2, 43740, 2, 1620, 270, 900, 90, 24300, 2, 500, 150, 131220, 2, 22500, 2, 24300, 4050, 4500, 2, 1968300, 10, 121500, 1350, 7500, 2, 112500, 810, 67500, 750, 22500, 2, 265720500, 2, 28, 3750, 364500, 450

Offset: 1

Antti Karttunen, Apr 27 2022

nonn

Index entries for sequences related to primorial base

Cf. A000010, A051953, A276085, A276086, A353563, A353565 (rgs-transform).

Cf. also A318834.

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353564(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A276086(eulerphi(d)))); m; };

a(1) = 1 (as an empty product).
a(n) = Product_{d|n, dA353563(d).
For all n >= 1, A276085(a(n)) = A051953(n).

A353565 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353564(i) = A353564(j), where A353564(n) = Product_{d|n, dA276086(phi(d)).

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 5, 6, 2, 7, 2, 8, 9, 7, 2, 10, 2, 11, 12, 10, 2, 13, 14, 15, 12, 16, 2, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 2, 26, 2, 22, 27, 28, 2, 29, 30, 31, 32, 33, 2, 34, 35, 36, 37, 26, 2, 38, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 47, 2, 48, 49, 50, 42, 51, 2, 52, 40, 53, 2, 54, 27, 55, 56, 47, 2, 57

Offset: 1

Antti Karttunen, Apr 27 2022

Restricted growth sequence transform of A353564.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A051953(i) = A051953(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A051953, A276086, A353563, A353564.

Cf. also A305800, A318835.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353564(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A276086(eulerphi(d)))); m; };
v353565 = rgs_transform(vector(up_to,n,A353564(n)));
A353565(n) = v353565[n];

cp's OEIS Frontend

A353564 Product_{d|n, dA276086(phi(d)), where A276086 is primorial base exp-function, and phi is Euler totient function.

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